The Tsallis distribution was introduced in 1988 by Constantino Tsallis as a generalization of the Boltzmann-Gibbs distribution and has been used in many fields of physics.
In high energy physics it has been used by several large experimental collaborations(PHENIX, STAR, ALICE, ATLAS, CMS, ...) and describes astonishingly well transverse momentum distributions in proton-proton collisions.
Figure 1. For high energy physics a consistent form of Tsallis statistics for the particle number, energy density and pressure is given by these three equations where T and μ are the temperature and the chemical potential, V is the volume and g is the degeneracy factor. The Tsallis distribution introduces a new parameter q which for transverse momentum spectra is always close to 1.
The Tsallis distribution introduces a new parameter q. In the limit where this parameter is 1 it reproduces the standard Boltzmann-Gibbs distribution. There are clear indications that this parameter increases very slowly with increasing beam energy and it has even been speculated that the increase in the transverse momentum distributions at higher energies is entirely due to the increase in this parameter.
Figure 2.Open symbols effective temperature T obtained using ALICE distribution. Closed symbols use Tsallis distribution. L.Marques, E.Andrade-II and A.Deppman arXiv: 1210.1725.
Clearly the Tsallis distribution plays a role in the description of high energy proton-proton collisions and further clarifications of its basic parameters will be central in developments.
Figure 3.Open symbols: parameter q obtained from the ALICE distribution. Closed symbols use Tsallis distribution. L.Marques, E.Andrade-II and A.Deppman arXiv: 1210.1725.